Question

A bumper sticker says, if you drive fast enough at a red light it will appear green. Determine how fast you would have to travel for a red light (442*10^12 Hz) to look green (566*10^12 Hz). Give your answer in m/s, miles per hour, and as a percentage of the speed of light. Using algebra.

Answer 1

We need to use the formula of Doppler shift for stationary source, moving observer.

f' = [(v + v₀)/v]*f

where,

  vo = Velocity of the Observer,

           v = Velocity of light in medium,

           f = Real frequency,

           f' = Apparent frequency.

Rearranging in terms of v₀ :

v_o = vf'/f - v

= [(3*10⁸)(566*10¹²)/(442*10¹²)] - (3*10⁸)

= 8.4 x 10⁷ m/s (ans)

In mph:

speed = 8.4 x 10⁷ x 2.24

= 1.88 x 10⁸ mph (ans)

As a percentage:

c = 3 x 10⁸ m/s

Thus,

v_o/c =(8.4 x 10⁷)/(3x10⁸)

v_o/c = 0.28

v_o = 0.28c (ans)